Abstract
AbstractWe consider a one-dimensional fluid-solid interaction model governed by the Burgers equation with a time varying interface. We discuss the inverse problem of determining the shape of the interface from Dirichlet and Neumann data at one endpoint of the spatial interval. In particular, we establish unique results and some conditional stability estimates. For the proofs, we use and adapt some lateral estimates that, in turn, rely on appropriate Carleman and interpolation inequalities.
Funder
Ministerio de Ciencia, Innovación y Universidades
Hezkuntza, Hizkuntza Politika Eta Kultura Saila, Eusko Jaurlaritza
Japan Society for the Promotion of Science
Publisher
Springer Science and Business Media LLC
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